Model Mathematics

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Component: environment

IP3_stim = \{\begin{matrix} 100 if time > 6 e -2 \land time < 7 e -2 \\ - 100 if time > 9 e -2 \land time < 10 e -2 \\ 0 otherwise \end{matrix}

\frac{d}{d time} (q_Ca_i) = ((((((v_R_IPR_main - v_R1_a_IPR - v_R2_a_IPR) + v_R3_a_IPR + v_R4_a_IPR - v_R5_a_IPR - v_R6_a_IPR) + v_R7_a_IPR + v_R8_a_IPR - v_R1_b_IPR - v_R2_b_IPR) + v_R3_b_IPR + v_R4_b_IPR - v_R5_b_IPR - v_R6_b_IPR) + v_R7_b_IPR + v_R8_b_IPR - v_R1_c_IPR - v_R2_c_IPR) + v_R3_c_IPR + v_R4_c_IPR - v_R5_c_IPR - v_R6_c_IPR) + v_R7_c_IPR + v_R8_c_IPR \frac{d}{d time} (q_Ca_SR) = - v_R_IPR_main \frac{d}{d time} (q_IP3) = ((((((- v_R9_a_IPR) + v_R10_a_IPR - v_R11_a_IPR) + v_R12_a_IPR - v_R9_b_IPR) + v_R10_b_IPR - v_R11_b_IPR) + v_R12_b_IPR - v_R9_c_IPR) + v_R10_c_IPR - v_R11_c_IPR) + v_R12_c_IPR + IP3_stim

Ca_gate = q_Sa_001_IPR + q_Sa_101_IPR + q_Sa_011_IPR + q_Sa_111_IPR + q_Sa_010_IPR + q_Sa_011_IPR + q_Sa_110_IPR + q_Sa_111_IPR + q_Sb_001_IPR + q_Sb_101_IPR + q_Sb_011_IPR + q_Sb_111_IPR + q_Sb_010_IPR + q_Sb_011_IPR + q_Sb_110_IPR + q_Sb_111_IPR + q_Sc_001_IPR + q_Sc_101_IPR + q_Sc_011_IPR + q_Sc_111_IPR + q_Sc_010_IPR + q_Sc_011_IPR + q_Sc_110_IPR + q_Sc_111_IPR Ca_tot = q_Ca_i + q_Ca_SR + Ca_gate

Component: IPR_parameters

Component: IPR

mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_Ca_SR = R T \ln (K_Ca_SR q_Ca_SR) mu_IP3 = R T \ln (K_IP3 q_IP3) mu_Sa_000_IPR = R T \ln (K_Sa_000_IPR q_Sa_000_IPR) mu_Sa_001_IPR = R T \ln (K_Sa_001_IPR q_Sa_001_IPR) mu_Sa_010_IPR = R T \ln (K_Sa_010_IPR q_Sa_010_IPR) mu_Sa_011_IPR = R T \ln (K_Sa_011_IPR q_Sa_011_IPR) mu_Sa_100_IPR = R T \ln (K_Sa_100_IPR q_Sa_100_IPR) mu_Sa_101_IPR = R T \ln (K_Sa_101_IPR q_Sa_101_IPR) mu_Sa_110_IPR = R T \ln (K_Sa_110_IPR q_Sa_110_IPR) mu_Sa_111_IPR = R T \ln (K_Sa_111_IPR q_Sa_111_IPR) mu_Sb_000_IPR = R T \ln (K_Sb_000_IPR q_Sb_000_IPR) mu_Sb_001_IPR = R T \ln (K_Sb_001_IPR q_Sb_001_IPR) mu_Sb_010_IPR = R T \ln (K_Sb_010_IPR q_Sb_010_IPR) mu_Sb_011_IPR = R T \ln (K_Sb_011_IPR q_Sb_011_IPR) mu_Sb_100_IPR = R T \ln (K_Sb_100_IPR q_Sb_100_IPR) mu_Sb_101_IPR = R T \ln (K_Sb_101_IPR q_Sb_101_IPR) mu_Sb_110_IPR = R T \ln (K_Sb_110_IPR q_Sb_110_IPR) mu_Sb_111_IPR = R T \ln (K_Sb_111_IPR q_Sb_111_IPR) mu_Sc_000_IPR = R T \ln (K_Sc_000_IPR q_Sc_000_IPR) mu_Sc_001_IPR = R T \ln (K_Sc_001_IPR q_Sc_001_IPR) mu_Sc_010_IPR = R T \ln (K_Sc_010_IPR q_Sc_010_IPR) mu_Sc_011_IPR = R T \ln (K_Sc_011_IPR q_Sc_011_IPR) mu_Sc_100_IPR = R T \ln (K_Sc_100_IPR q_Sc_100_IPR) mu_Sc_101_IPR = R T \ln (K_Sc_101_IPR q_Sc_101_IPR) mu_Sc_110_IPR = R T \ln (K_Sc_110_IPR q_Sc_110_IPR) mu_Sc_111_IPR = R T \ln (K_Sc_111_IPR q_Sc_111_IPR) v_R_IPR_main_nogate = kappa_R_IPR_main (ⅇ^{\frac{mu_Ca_SR}{R T}} - (ⅇ^{\frac{mu_Ca_i}{R T}})) v_R_IPR_main = kappa_R_IPR_main (ⅇ^{\frac{mu_Ca_SR + mu_Sa_110_IPR + mu_Sb_110_IPR + mu_Sc_110_IPR}{R T}} - (ⅇ^{\frac{mu_Ca_i + mu_Sa_110_IPR + mu_Sb_110_IPR + mu_Sc_110_IPR}{R T}})) v_R1_a_IPR = kappa_R1_a_IPR (ⅇ^{\frac{mu_Sa_000_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sa_001_IPR}{R T}})) v_R2_a_IPR = kappa_R2_a_IPR (ⅇ^{\frac{mu_Sa_001_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sa_011_IPR}{R T}})) v_R3_a_IPR = kappa_R3_a_IPR (ⅇ^{\frac{mu_Sa_011_IPR}{R T}} - (ⅇ^{\frac{mu_Sa_010_IPR + mu_Ca_i}{R T}})) v_R4_a_IPR = kappa_R4_a_IPR (ⅇ^{\frac{mu_Sa_010_IPR}{R T}} - (ⅇ^{\frac{mu_Sa_000_IPR + mu_Ca_i}{R T}})) v_R5_a_IPR = kappa_R5_a_IPR (ⅇ^{\frac{mu_Sa_100_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sa_101_IPR}{R T}})) v_R6_a_IPR = kappa_R6_a_IPR (ⅇ^{\frac{mu_Sa_101_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sa_111_IPR}{R T}})) v_R7_a_IPR = kappa_R7_a_IPR (ⅇ^{\frac{mu_Sa_111_IPR}{R T}} - (ⅇ^{\frac{mu_Sa_110_IPR + mu_Ca_i}{R T}})) v_R8_a_IPR = kappa_R8_a_IPR (ⅇ^{\frac{mu_Sa_110_IPR}{R T}} - (ⅇ^{\frac{mu_Sa_100_IPR + mu_Ca_i}{R T}})) v_R9_a_IPR = kappa_R9_a_IPR (ⅇ^{\frac{mu_Sa_001_IPR + mu_IP3}{R T}} - (ⅇ^{\frac{mu_Sa_101_IPR}{R T}})) v_R10_a_IPR = kappa_R10_a_IPR (ⅇ^{\frac{mu_Sa_100_IPR}{R T}} - (ⅇ^{\frac{mu_Sa_000_IPR + mu_IP3}{R T}})) v_R11_a_IPR = kappa_R11_a_IPR (ⅇ^{\frac{mu_Sa_011_IPR + mu_IP3}{R T}} - (ⅇ^{\frac{mu_Sa_111_IPR}{R T}})) v_R12_a_IPR = kappa_R12_a_IPR (ⅇ^{\frac{mu_Sa_110_IPR}{R T}} - (ⅇ^{\frac{mu_Sa_010_IPR + mu_IP3}{R T}})) v_R1_b_IPR = kappa_R1_b_IPR (ⅇ^{\frac{mu_Sb_000_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sb_001_IPR}{R T}})) v_R2_b_IPR = kappa_R2_b_IPR (ⅇ^{\frac{mu_Sb_001_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sb_011_IPR}{R T}})) v_R3_b_IPR = kappa_R3_b_IPR (ⅇ^{\frac{mu_Sb_011_IPR}{R T}} - (ⅇ^{\frac{mu_Sb_010_IPR + mu_Ca_i}{R T}})) v_R4_b_IPR = kappa_R4_b_IPR (ⅇ^{\frac{mu_Sb_010_IPR}{R T}} - (ⅇ^{\frac{mu_Sb_000_IPR + mu_Ca_i}{R T}})) v_R5_b_IPR = kappa_R5_b_IPR (ⅇ^{\frac{mu_Sb_100_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sb_101_IPR}{R T}})) v_R6_b_IPR = kappa_R6_b_IPR (ⅇ^{\frac{mu_Sb_101_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sb_111_IPR}{R T}})) v_R7_b_IPR = kappa_R7_b_IPR (ⅇ^{\frac{mu_Sb_111_IPR}{R T}} - (ⅇ^{\frac{mu_Sb_110_IPR + mu_Ca_i}{R T}})) v_R8_b_IPR = kappa_R8_b_IPR (ⅇ^{\frac{mu_Sb_110_IPR}{R T}} - (ⅇ^{\frac{mu_Sb_100_IPR + mu_Ca_i}{R T}})) v_R9_b_IPR = kappa_R9_b_IPR (ⅇ^{\frac{mu_Sb_001_IPR + mu_IP3}{R T}} - (ⅇ^{\frac{mu_Sb_101_IPR}{R T}})) v_R10_b_IPR = kappa_R10_b_IPR (ⅇ^{\frac{mu_Sb_100_IPR}{R T}} - (ⅇ^{\frac{mu_Sb_000_IPR + mu_IP3}{R T}})) v_R11_b_IPR = kappa_R11_b_IPR (ⅇ^{\frac{mu_Sb_011_IPR + mu_IP3}{R T}} - (ⅇ^{\frac{mu_Sb_111_IPR}{R T}})) v_R12_b_IPR = kappa_R12_b_IPR (ⅇ^{\frac{mu_Sb_110_IPR}{R T}} - (ⅇ^{\frac{mu_Sb_010_IPR + mu_IP3}{R T}})) v_R1_c_IPR = kappa_R1_c_IPR (ⅇ^{\frac{mu_Sc_000_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sc_001_IPR}{R T}})) v_R2_c_IPR = kappa_R2_c_IPR (ⅇ^{\frac{mu_Sc_001_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sc_011_IPR}{R T}})) v_R3_c_IPR = kappa_R3_c_IPR (ⅇ^{\frac{mu_Sc_011_IPR}{R T}} - (ⅇ^{\frac{mu_Sc_010_IPR + mu_Ca_i}{R T}})) v_R4_c_IPR = kappa_R4_c_IPR (ⅇ^{\frac{mu_Sc_010_IPR}{R T}} - (ⅇ^{\frac{mu_Sc_000_IPR + mu_Ca_i}{R T}})) v_R5_c_IPR = kappa_R5_c_IPR (ⅇ^{\frac{mu_Sc_100_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sc_101_IPR}{R T}})) v_R6_c_IPR = kappa_R6_c_IPR (ⅇ^{\frac{mu_Sc_101_IPR + mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Sc_111_IPR}{R T}})) v_R7_c_IPR = kappa_R7_c_IPR (ⅇ^{\frac{mu_Sc_111_IPR}{R T}} - (ⅇ^{\frac{mu_Sc_110_IPR + mu_Ca_i}{R T}})) v_R8_c_IPR = kappa_R8_c_IPR (ⅇ^{\frac{mu_Sc_110_IPR}{R T}} - (ⅇ^{\frac{mu_Sc_100_IPR + mu_Ca_i}{R T}})) v_R9_c_IPR = kappa_R9_c_IPR (ⅇ^{\frac{mu_Sc_001_IPR + mu_IP3}{R T}} - (ⅇ^{\frac{mu_Sc_101_IPR}{R T}})) v_R10_c_IPR = kappa_R10_c_IPR (ⅇ^{\frac{mu_Sc_100_IPR}{R T}} - (ⅇ^{\frac{mu_Sc_000_IPR + mu_IP3}{R T}})) v_R11_c_IPR = kappa_R11_c_IPR (ⅇ^{\frac{mu_Sc_011_IPR + mu_IP3}{R T}} - (ⅇ^{\frac{mu_Sc_111_IPR}{R T}})) v_R12_c_IPR = kappa_R12_c_IPR (ⅇ^{\frac{mu_Sc_110_IPR}{R T}} - (ⅇ^{\frac{mu_Sc_010_IPR + mu_IP3}{R T}})) \frac{d}{d time} (q_Sa_000_IPR) = (- v_R1_a_IPR) + v_R4_a_IPR + v_R10_a_IPR \frac{d}{d time} (q_Sa_001_IPR) = v_R1_a_IPR - v_R2_a_IPR - v_R9_a_IPR \frac{d}{d time} (q_Sa_010_IPR) = (v_R3_a_IPR - v_R4_a_IPR) + v_R12_a_IPR \frac{d}{d time} (q_Sa_011_IPR) = v_R2_a_IPR - v_R3_a_IPR - v_R11_a_IPR \frac{d}{d time} (q_Sa_100_IPR) = (- v_R5_a_IPR) + v_R8_a_IPR - v_R10_a_IPR \frac{d}{d time} (q_Sa_101_IPR) = (v_R5_a_IPR - v_R6_a_IPR) + v_R9_a_IPR \frac{d}{d time} (q_Sa_110_IPR) = v_R7_a_IPR - v_R8_a_IPR - v_R12_a_IPR \frac{d}{d time} (q_Sa_111_IPR) = (v_R6_a_IPR - v_R7_a_IPR) + v_R11_a_IPR \frac{d}{d time} (q_Sb_000_IPR) = (- v_R1_b_IPR) + v_R4_b_IPR + v_R10_b_IPR \frac{d}{d time} (q_Sb_001_IPR) = v_R1_b_IPR - v_R2_b_IPR - v_R9_b_IPR \frac{d}{d time} (q_Sb_010_IPR) = (v_R3_b_IPR - v_R4_b_IPR) + v_R12_b_IPR \frac{d}{d time} (q_Sb_011_IPR) = v_R2_b_IPR - v_R3_b_IPR - v_R11_b_IPR \frac{d}{d time} (q_Sb_100_IPR) = (- v_R5_b_IPR) + v_R8_b_IPR - v_R10_b_IPR \frac{d}{d time} (q_Sb_101_IPR) = (v_R5_b_IPR - v_R6_b_IPR) + v_R9_b_IPR \frac{d}{d time} (q_Sb_110_IPR) = v_R7_b_IPR - v_R8_b_IPR - v_R12_b_IPR \frac{d}{d time} (q_Sb_111_IPR) = (v_R6_b_IPR - v_R7_b_IPR) + v_R11_b_IPR \frac{d}{d time} (q_Sc_000_IPR) = (- v_R1_c_IPR) + v_R4_c_IPR + v_R10_c_IPR \frac{d}{d time} (q_Sc_001_IPR) = v_R1_c_IPR - v_R2_c_IPR - v_R9_c_IPR \frac{d}{d time} (q_Sc_010_IPR) = (v_R3_c_IPR - v_R4_c_IPR) + v_R12_c_IPR \frac{d}{d time} (q_Sc_011_IPR) = v_R2_c_IPR - v_R3_c_IPR - v_R11_c_IPR \frac{d}{d time} (q_Sc_100_IPR) = (- v_R5_c_IPR) + v_R8_c_IPR - v_R10_c_IPR \frac{d}{d time} (q_Sc_101_IPR) = (v_R5_c_IPR - v_R6_c_IPR) + v_R9_c_IPR \frac{d}{d time} (q_Sc_110_IPR) = v_R7_c_IPR - v_R8_c_IPR - v_R12_c_IPR \frac{d}{d time} (q_Sc_111_IPR) = (v_R6_c_IPR - v_R7_c_IPR) + v_R11_c_IPR

Model Mathematics

Component: environment

Component: IPR_parameters

Component: IPR

Component: units

Component: constants